For our trials we constrain \(A\)  to be symmetric for the VBE, and apply no constraints for the KSE. We chose to limit the constraints applied to the neural ODE because the underlying systems possesses nonlinear stability in the form of an inertial manifold. We took this approach to show that the model can learn this property from the data when the neural ODE is provided a linear term. An alternative future direction is explicitly enforcing the existence of an inertial manifold. This could be done by enforcing a spectral gap condition, which guarantees the existence of an inertial manifold [1]}. The spectral gap condition is
\(\lambda _{N+1}-\lambda _{N}>2 L\) 
